/*
 * Copyright (c) 2003, 2006, Oracle and/or its affiliates. All rights reserved.
 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
 *
 * This code is free software; you can redistribute it and/or modify it
 * under the terms of the GNU General Public License version 2 only, as
 * published by the Free Software Foundation.  Oracle designates this
 * particular file as subject to the "Classpath" exception as provided
 * by Oracle in the LICENSE file that accompanied this code.
 *
 * This code is distributed in the hope that it will be useful, but WITHOUT
 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
 * version 2 for more details (a copy is included in the LICENSE file that
 * accompanied this code).
 *
 * You should have received a copy of the GNU General Public License version
 * 2 along with this work; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
 *
 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
 * or visit www.oracle.com if you need additional information or have any
 * questions.
 */

package com.sun.tools.javac.code;

import static com.sun.tools.javac.code.Flags.ABSTRACT;
import static com.sun.tools.javac.code.Flags.ACYCLIC;
import static com.sun.tools.javac.code.Flags.COMPOUND;
import static com.sun.tools.javac.code.Flags.FINAL;
import static com.sun.tools.javac.code.Flags.INTERFACE;
import static com.sun.tools.javac.code.Flags.PUBLIC;
import static com.sun.tools.javac.code.Flags.STATIC;
import static com.sun.tools.javac.code.Flags.SYNTHETIC;
import static com.sun.tools.javac.code.Type.map;
import static com.sun.tools.javac.code.TypeTags.ARRAY;
import static com.sun.tools.javac.code.TypeTags.BOOLEAN;
import static com.sun.tools.javac.code.TypeTags.BOT;
import static com.sun.tools.javac.code.TypeTags.BYTE;
import static com.sun.tools.javac.code.TypeTags.CHAR;
import static com.sun.tools.javac.code.TypeTags.CLASS;
import static com.sun.tools.javac.code.TypeTags.DOUBLE;
import static com.sun.tools.javac.code.TypeTags.ERROR;
import static com.sun.tools.javac.code.TypeTags.FLOAT;
import static com.sun.tools.javac.code.TypeTags.FORALL;
import static com.sun.tools.javac.code.TypeTags.INT;
import static com.sun.tools.javac.code.TypeTags.LONG;
import static com.sun.tools.javac.code.TypeTags.METHOD;
import static com.sun.tools.javac.code.TypeTags.NONE;
import static com.sun.tools.javac.code.TypeTags.SHORT;
import static com.sun.tools.javac.code.TypeTags.TYPEVAR;
import static com.sun.tools.javac.code.TypeTags.UNDETVAR;
import static com.sun.tools.javac.code.TypeTags.UNKNOWN;
import static com.sun.tools.javac.code.TypeTags.VOID;
import static com.sun.tools.javac.code.TypeTags.WILDCARD;
import static com.sun.tools.javac.code.TypeTags.firstPartialTag;
import static com.sun.tools.javac.code.TypeTags.lastBaseTag;
import static com.sun.tools.javac.util.ListBuffer.lb;

import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;

import android.annotation.SuppressLint;

import com.sun.tools.javac.code.Symbol.ClassSymbol;
import com.sun.tools.javac.code.Type.ArrayType;
import com.sun.tools.javac.code.Type.CapturedType;
import com.sun.tools.javac.code.Type.ClassType;
import com.sun.tools.javac.code.Type.ErrorType;
import com.sun.tools.javac.code.Type.ForAll;
import com.sun.tools.javac.code.Type.Mapping;
import com.sun.tools.javac.code.Type.MethodType;
import com.sun.tools.javac.code.Type.PackageType;
import com.sun.tools.javac.code.Type.TypeVar;
import com.sun.tools.javac.code.Type.UndetVar;
import com.sun.tools.javac.code.Type.WildcardType;
import com.sun.tools.javac.comp.Check;
import com.sun.tools.javac.jvm.ClassReader;
import com.sun.tools.javac.util.Context;
import com.sun.tools.javac.util.List;
import com.sun.tools.javac.util.ListBuffer;
import com.sun.tools.javac.util.Name;
import com.sun.tools.javac.util.Warner;

/**
 * Utility class containing various operations on types.
 * 
 * <p>
 * Unless other names are more illustrative, the following naming conventions
 * should be observed in this file:
 * 
 * <dl>
 * <dt>t</dt>
 * <dd>If the first argument to an operation is a type, it should be named t.</dd>
 * <dt>s</dt>
 * <dd>Similarly, if the second argument to an operation is a type, it should be
 * named s.</dd>
 * <dt>ts</dt>
 * <dd>If an operations takes a list of types, the first should be named ts.</dd>
 * <dt>ss</dt>
 * <dd>A second list of types should be named ss.</dd>
 * </dl>
 * 
 * <p>
 * <b>This is NOT part of any supported API. If you write code that depends on
 * this, you do so at your own risk. This code and its internal interfaces are
 * subject to change or deletion without notice.</b>
 */
@SuppressLint("Assert") public class Types {
	protected static final Context.Key<Types> typesKey = new Context.Key<Types>();

	final Symtab syms;
	final Name.Table names;
	final boolean allowBoxing;
	final ClassReader reader;
	final Source source;
	final Check chk;
	List<Warner> warnStack = List.nil();
	final Name capturedName;

	// <editor-fold defaultstate="collapsed" desc="Instantiating">
	public static Types instance(Context context) {
		Types instance = context.get(typesKey);
		if (instance == null)
			instance = new Types(context);
		return instance;
	}

	protected Types(Context context) {
		context.put(typesKey, this);
		syms = Symtab.instance(context);
		names = Name.Table.instance(context);
		allowBoxing = Source.instance(context).allowBoxing();
		reader = ClassReader.instance(context);
		source = Source.instance(context);
		chk = Check.instance(context);
		capturedName = names.fromString("<captured wildcard>");
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="upperBound">
	/**
	 * The "rvalue conversion".<br>
	 * The upper bound of most types is the type itself. Wildcards, on the other
	 * hand have upper and lower bounds.
	 * 
	 * @param t
	 *            a type
	 * @return the upper bound of the given type
	 */
	public Type upperBound(Type t) {
		return upperBound.visit(t);
	}

	// where
	private final MapVisitor<Void> upperBound = new MapVisitor<Void>() {

		@Override
		public Type visitWildcardType(WildcardType t, Void ignored) {
			if (t.isSuperBound())
				return t.bound == null ? syms.objectType : t.bound.bound;
			else
				return visit(t.type);
		}

		@Override
		public Type visitCapturedType(CapturedType t, Void ignored) {
			return visit(t.bound);
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="lowerBound">
	/**
	 * The "lvalue conversion".<br>
	 * The lower bound of most types is the type itself. Wildcards, on the other
	 * hand have upper and lower bounds.
	 * 
	 * @param t
	 *            a type
	 * @return the lower bound of the given type
	 */
	public Type lowerBound(Type t) {
		return lowerBound.visit(t);
	}

	// where
	private final MapVisitor<Void> lowerBound = new MapVisitor<Void>() {

		@Override
		public Type visitWildcardType(WildcardType t, Void ignored) {
			return t.isExtendsBound() ? syms.botType : visit(t.type);
		}

		@Override
		public Type visitCapturedType(CapturedType t, Void ignored) {
			return visit(t.getLowerBound());
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isUnbounded">
	/**
	 * Checks that all the arguments to a class are unbounded wildcards or
	 * something else that doesn't make any restrictions on the arguments. If a
	 * class isUnbounded, a raw super- or subclass can be cast to it without a
	 * warning.
	 * 
	 * @param t
	 *            a type
	 * @return true iff the given type is unbounded or raw
	 */
	public boolean isUnbounded(Type t) {
		return isUnbounded.visit(t);
	}

	// where
	private final UnaryVisitor<Boolean> isUnbounded = new UnaryVisitor<Boolean>() {

		public Boolean visitType(Type t, Void ignored) {
			return true;
		}

		@Override
		public Boolean visitClassType(ClassType t, Void ignored) {
			List<Type> parms = t.tsym.type.allparams();
			List<Type> args = t.allparams();
			while (parms.nonEmpty()) {
				WildcardType unb = new WildcardType(syms.objectType,
						BoundKind.UNBOUND, syms.boundClass,
						(TypeVar) parms.head);
				if (!containsType(args.head, unb))
					return false;
				parms = parms.tail;
				args = args.tail;
			}
			return true;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="asSub">
	/**
	 * Return the least specific subtype of t that starts with symbol sym. If
	 * none exists, return null. The least specific subtype is determined as
	 * follows:
	 * 
	 * <p>
	 * If there is exactly one parameterized instance of sym that is a subtype
	 * of t, that parameterized instance is returned.<br>
	 * Otherwise, if the plain type or raw type `sym' is a subtype of type t,
	 * the type `sym' itself is returned. Otherwise, null is returned.
	 */
	public Type asSub(Type t, Symbol sym) {
		return asSub.visit(t, sym);
	}

	// where
	private final SimpleVisitor<Type, Symbol> asSub = new SimpleVisitor<Type, Symbol>() {

		public Type visitType(Type t, Symbol sym) {
			return null;
		}

		@Override
		public Type visitClassType(ClassType t, Symbol sym) {
			if (t.tsym == sym)
				return t;
			Type base = asSuper(sym.type, t.tsym);
			if (base == null)
				return null;
			ListBuffer<Type> from = new ListBuffer<Type>();
			ListBuffer<Type> to = new ListBuffer<Type>();
			try {
				adapt(base, t, from, to);
			} catch (AdaptFailure ex) {
				return null;
			}
			Type res = subst(sym.type, from.toList(), to.toList());
			if (!isSubtype(res, t))
				return null;
			ListBuffer<Type> openVars = new ListBuffer<Type>();
			for (List<Type> l = sym.type.allparams(); l.nonEmpty(); l = l.tail)
				if (res.contains(l.head) && !t.contains(l.head))
					openVars.append(l.head);
			if (openVars.nonEmpty()) {
				if (t.isRaw()) {
					// The subtype of a raw type is raw
					res = erasure(res);
				} else {
					// Unbound type arguments default to ?
					List<Type> opens = openVars.toList();
					ListBuffer<Type> qs = new ListBuffer<Type>();
					for (List<Type> iter = opens; iter.nonEmpty(); iter = iter.tail) {
						qs.append(new WildcardType(syms.objectType,
								BoundKind.UNBOUND, syms.boundClass,
								(TypeVar) iter.head));
					}
					res = subst(res, opens, qs.toList());
				}
			}
			return res;
		}

		@Override
		public Type visitErrorType(ErrorType t, Symbol sym) {
			return t;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isConvertible">
	/**
	 * Is t a subtype of or convertiable via boxing/unboxing convertions to s?
	 */
	public boolean isConvertible(Type t, Type s, Warner warn) {
		boolean tPrimitive = t.isPrimitive();
		boolean sPrimitive = s.isPrimitive();
		if (tPrimitive == sPrimitive)
			return isSubtypeUnchecked(t, s, warn);
		if (!allowBoxing)
			return false;
		return tPrimitive ? isSubtype(boxedClass(t).type, s) : isSubtype(
				unboxedType(t), s);
	}

	/**
	 * Is t a subtype of or convertiable via boxing/unboxing convertions to s?
	 */
	public boolean isConvertible(Type t, Type s) {
		return isConvertible(t, s, Warner.noWarnings);
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isSubtype">
	/**
	 * Is t an unchecked subtype of s?
	 */
	public boolean isSubtypeUnchecked(Type t, Type s) {
		return isSubtypeUnchecked(t, s, Warner.noWarnings);
	}

	/**
	 * Is t an unchecked subtype of s?
	 */
	public boolean isSubtypeUnchecked(Type t, Type s, Warner warn) {
		if (t.tag == ARRAY && s.tag == ARRAY) {
			return (((ArrayType) t).elemtype.tag <= lastBaseTag) ? isSameType(
					elemtype(t), elemtype(s)) : isSubtypeUnchecked(elemtype(t),
					elemtype(s), warn);
		} else if (isSubtype(t, s)) {
			return true;
		} else if (!s.isRaw()) {
			Type t2 = asSuper(t, s.tsym);
			if (t2 != null && t2.isRaw()) {
				if (isReifiable(s))
					warn.silentUnchecked();
				else
					warn.warnUnchecked();
				return true;
			}
		}
		return false;
	}

	/**
	 * Is t a subtype of s?<br>
	 * (not defined for Method and ForAll types)
	 */
	final public boolean isSubtype(Type t, Type s) {
		return isSubtype(t, s, true);
	}

	final public boolean isSubtypeNoCapture(Type t, Type s) {
		return isSubtype(t, s, false);
	}

	public boolean isSubtype(Type t, Type s, boolean capture) {
		if (t == s)
			return true;

		if (s.tag >= firstPartialTag)
			return isSuperType(s, t);

		Type lower = lowerBound(s);
		if (s != lower)
			return isSubtype(capture ? capture(t) : t, lower, false);

		return isSubtype.visit(capture ? capture(t) : t, s);
	}

	// where
	private TypeRelation isSubtype = new TypeRelation() {
		public Boolean visitType(Type t, Type s) {
			switch (t.tag) {
			case BYTE:
			case CHAR:
				return (t.tag == s.tag || t.tag + 2 <= s.tag && s.tag <= DOUBLE);
			case SHORT:
			case INT:
			case LONG:
			case FLOAT:
			case DOUBLE:
				return t.tag <= s.tag && s.tag <= DOUBLE;
			case BOOLEAN:
			case VOID:
				return t.tag == s.tag;
			case TYPEVAR:
				return isSubtypeNoCapture(t.getUpperBound(), s);
			case BOT:
				return s.tag == BOT || s.tag == CLASS || s.tag == ARRAY
						|| s.tag == TYPEVAR;
			case NONE:
				return false;
			default:
				throw new AssertionError("isSubtype " + t.tag);
			}
		}

		private Set<TypePair> cache = new HashSet<TypePair>();

		private boolean containsTypeRecursive(Type t, Type s) {
			TypePair pair = new TypePair(t, s);
			if (cache.add(pair)) {
				try {
					return containsType(t.getTypeArguments(),
							s.getTypeArguments());
				} finally {
					cache.remove(pair);
				}
			} else {
				return containsType(t.getTypeArguments(), rewriteSupers(s)
						.getTypeArguments());
			}
		}

		private Type rewriteSupers(Type t) {
			if (!t.isParameterized())
				return t;
			ListBuffer<Type> from = lb();
			ListBuffer<Type> to = lb();
			adaptSelf(t, from, to);
			if (from.isEmpty())
				return t;
			ListBuffer<Type> rewrite = lb();
			boolean changed = false;
			for (Type orig : to.toList()) {
				Type s = rewriteSupers(orig);
				if (s.isSuperBound() && !s.isExtendsBound()) {
					s = new WildcardType(syms.objectType, BoundKind.UNBOUND,
							syms.boundClass);
					changed = true;
				} else if (s != orig) {
					s = new WildcardType(upperBound(s), BoundKind.EXTENDS,
							syms.boundClass);
					changed = true;
				}
				rewrite.append(s);
			}
			if (changed)
				return subst(t.tsym.type, from.toList(), rewrite.toList());
			else
				return t;
		}

		@Override
		public Boolean visitClassType(ClassType t, Type s) {
			Type sup = asSuper(t, s.tsym);
			return sup != null
					&& sup.tsym == s.tsym
					// You're not allowed to write
					// Vector<Object> vec = new Vector<String>();
					// But with wildcards you can write
					// Vector<? extends Object> vec = new Vector<String>();
					// which means that subtype checking must be done
					// here instead of same-type checking (via containsType).
					&& (!s.isParameterized() || containsTypeRecursive(s, sup))
					&& isSubtypeNoCapture(sup.getEnclosingType(),
							s.getEnclosingType());
		}

		@Override
		public Boolean visitArrayType(ArrayType t, Type s) {
			if (s.tag == ARRAY) {
				if (t.elemtype.tag <= lastBaseTag)
					return isSameType(t.elemtype, elemtype(s));
				else
					return isSubtypeNoCapture(t.elemtype, elemtype(s));
			}

			if (s.tag == CLASS) {
				Name sname = s.tsym.getQualifiedName();
				return sname == names.java_lang_Object
						|| sname == names.java_lang_Cloneable
						|| sname == names.java_io_Serializable;
			}

			return false;
		}

		@Override
		public Boolean visitUndetVar(UndetVar t, Type s) {
			// todo: test against origin needed? or replace with substitution?
			if (t == s || t.qtype == s || s.tag == ERROR || s.tag == UNKNOWN)
				return true;

			if (t.inst != null)
				return isSubtypeNoCapture(t.inst, s); // TODO: ", warn"?

			t.hibounds = t.hibounds.prepend(s);
			return true;
		}

		@Override
		public Boolean visitErrorType(ErrorType t, Type s) {
			return true;
		}
	};

	/**
	 * Is t a subtype of every type in given list `ts'?<br>
	 * (not defined for Method and ForAll types)<br>
	 * Allows unchecked conversions.
	 */
	public boolean isSubtypeUnchecked(Type t, List<Type> ts, Warner warn) {
		for (List<Type> l = ts; l.nonEmpty(); l = l.tail)
			if (!isSubtypeUnchecked(t, l.head, warn))
				return false;
		return true;
	}

	/**
	 * Are corresponding elements of ts subtypes of ss? If lists are of
	 * different length, return false.
	 */
	public boolean isSubtypes(List<Type> ts, List<Type> ss) {
		while (ts.tail != null
				&& ss.tail != null
				/* inlined: ts.nonEmpty() && ss.nonEmpty() */&& isSubtype(
						ts.head, ss.head)) {
			ts = ts.tail;
			ss = ss.tail;
		}
		return ts.tail == null && ss.tail == null;
		/* inlined: ts.isEmpty() && ss.isEmpty(); */
	}

	/**
	 * Are corresponding elements of ts subtypes of ss, allowing unchecked
	 * conversions? If lists are of different length, return false.
	 **/
	public boolean isSubtypesUnchecked(List<Type> ts, List<Type> ss, Warner warn) {
		while (ts.tail != null
				&& ss.tail != null
				/* inlined: ts.nonEmpty() && ss.nonEmpty() */&& isSubtypeUnchecked(
						ts.head, ss.head, warn)) {
			ts = ts.tail;
			ss = ss.tail;
		}
		return ts.tail == null && ss.tail == null;
		/* inlined: ts.isEmpty() && ss.isEmpty(); */
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isSuperType">
	/**
	 * Is t a supertype of s?
	 */
	public boolean isSuperType(Type t, Type s) {
		switch (t.tag) {
		case ERROR:
			return true;
		case UNDETVAR: {
			UndetVar undet = (UndetVar) t;
			if (t == s || undet.qtype == s || s.tag == ERROR || s.tag == BOT)
				return true;
			if (undet.inst != null)
				return isSubtype(s, undet.inst);
			undet.lobounds = undet.lobounds.prepend(s);
			return true;
		}
		default:
			return isSubtype(s, t);
		}
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isSameType">
	/**
	 * Are corresponding elements of the lists the same type? If lists are of
	 * different length, return false.
	 */
	public boolean isSameTypes(List<Type> ts, List<Type> ss) {
		while (ts.tail != null
				&& ss.tail != null
				/* inlined: ts.nonEmpty() && ss.nonEmpty() */&& isSameType(
						ts.head, ss.head)) {
			ts = ts.tail;
			ss = ss.tail;
		}
		return ts.tail == null && ss.tail == null;
		/* inlined: ts.isEmpty() && ss.isEmpty(); */
	}

	/**
	 * Is t the same type as s?
	 */
	public boolean isSameType(Type t, Type s) {
		return isSameType.visit(t, s);
	}

	// where
	private TypeRelation isSameType = new TypeRelation() {

		public Boolean visitType(Type t, Type s) {
			if (t == s)
				return true;

			if (s.tag >= firstPartialTag)
				return visit(s, t);

			switch (t.tag) {
			case BYTE:
			case CHAR:
			case SHORT:
			case INT:
			case LONG:
			case FLOAT:
			case DOUBLE:
			case BOOLEAN:
			case VOID:
			case BOT:
			case NONE:
				return t.tag == s.tag;
			case TYPEVAR:
				return s.isSuperBound() && !s.isExtendsBound()
						&& visit(t, upperBound(s));
			default:
				throw new AssertionError("isSameType " + t.tag);
			}
		}

		@Override
		public Boolean visitWildcardType(WildcardType t, Type s) {
			if (s.tag >= firstPartialTag)
				return visit(s, t);
			else
				return false;
		}

		@Override
		public Boolean visitClassType(ClassType t, Type s) {
			if (t == s)
				return true;

			if (s.tag >= firstPartialTag)
				return visit(s, t);

			if (s.isSuperBound() && !s.isExtendsBound())
				return visit(t, upperBound(s)) && visit(t, lowerBound(s));

			if (t.isCompound() && s.isCompound()) {
				if (!visit(supertype(t), supertype(s)))
					return false;

				HashSet<SingletonType> set = new HashSet<SingletonType>();
				for (Type x : interfaces(t))
					set.add(new SingletonType(x));
				for (Type x : interfaces(s)) {
					if (!set.remove(new SingletonType(x)))
						return false;
				}
				return (set.size() == 0);
			}
			return t.tsym == s.tsym
					&& visit(t.getEnclosingType(), s.getEnclosingType())
					&& containsTypeEquivalent(t.getTypeArguments(),
							s.getTypeArguments());
		}

		@Override
		public Boolean visitArrayType(ArrayType t, Type s) {
			if (t == s)
				return true;

			if (s.tag >= firstPartialTag)
				return visit(s, t);

			return s.tag == ARRAY
					&& containsTypeEquivalent(t.elemtype, elemtype(s));
		}

		@Override
		public Boolean visitMethodType(MethodType t, Type s) {
			// isSameType for methods does not take thrown
			// exceptions into account!
			return hasSameArgs(t, s)
					&& visit(t.getReturnType(), s.getReturnType());
		}

		@Override
		public Boolean visitPackageType(PackageType t, Type s) {
			return t == s;
		}

		@Override
		public Boolean visitForAll(ForAll t, Type s) {
			if (s.tag != FORALL)
				return false;

			ForAll forAll = (ForAll) s;
			return hasSameBounds(t, forAll)
					&& visit(t.qtype,
							subst(forAll.qtype, forAll.tvars, t.tvars));
		}

		@Override
		public Boolean visitUndetVar(UndetVar t, Type s) {
			if (s.tag == WILDCARD)
				// FIXME, this might be leftovers from before capture conversion
				return false;

			if (t == s || t.qtype == s || s.tag == ERROR || s.tag == UNKNOWN)
				return true;

			if (t.inst != null)
				return visit(t.inst, s);

			t.inst = fromUnknownFun.apply(s);
			for (List<Type> l = t.lobounds; l.nonEmpty(); l = l.tail) {
				if (!isSubtype(l.head, t.inst))
					return false;
			}
			for (List<Type> l = t.hibounds; l.nonEmpty(); l = l.tail) {
				if (!isSubtype(t.inst, l.head))
					return false;
			}
			return true;
		}

		@Override
		public Boolean visitErrorType(ErrorType t, Type s) {
			return true;
		}
	};
	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="fromUnknownFun">
	/**
	 * A mapping that turns all unknown types in this type to fresh unknown
	 * variables.
	 */
	public Mapping fromUnknownFun = new Mapping("fromUnknownFun") {
		public Type apply(Type t) {
			if (t.tag == UNKNOWN)
				return new UndetVar(t);
			else
				return t.map(this);
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="Contains Type">
	public boolean containedBy(Type t, Type s) {
		switch (t.tag) {
		case UNDETVAR:
			if (s.tag == WILDCARD) {
				UndetVar undetvar = (UndetVar) t;

				// Because of wildcard capture, s must be on the left
				// hand side of an assignment. Furthermore, t is an
				// underconstrained type variable, for example, one
				// that is only used in the return type of a method.
				// If the type variable is truly underconstrained, it
				// cannot have any low bounds:
				assert undetvar.lobounds.isEmpty() : undetvar;

				undetvar.inst = glb(upperBound(s), undetvar.inst);
				return true;
			} else {
				return isSameType(t, s);
			}
		case ERROR:
			return true;
		default:
			return containsType(s, t);
		}
	}

	boolean containsType(List<Type> ts, List<Type> ss) {
		while (ts.nonEmpty() && ss.nonEmpty() && containsType(ts.head, ss.head)) {
			ts = ts.tail;
			ss = ss.tail;
		}
		return ts.isEmpty() && ss.isEmpty();
	}

	/**
	 * Check if t contains s.
	 * 
	 * <p>
	 * T contains S if:
	 * 
	 * <p>
	 * {@code L(T) <: L(S) && U(S) <: U(T)}
	 * 
	 * <p>
	 * This relation is only used by ClassType.isSubtype(), that is,
	 * 
	 * <p>
	 * {@code C<S> <: C<T> if T contains S.}
	 * 
	 * <p>
	 * Because of F-bounds, this relation can lead to infinite recursion. Thus
	 * we must somehow break that recursion. Notice that containsType() is only
	 * called from ClassType.isSubtype(). Since the arguments have already been
	 * checked against their bounds, we know:
	 * 
	 * <p>
	 * {@code U(S) <: U(T) if T is "super" bound (U(T) *is* the bound)}
	 * 
	 * <p>
	 * {@code L(T) <: L(S) if T is "extends" bound (L(T) is bottom)}
	 * 
	 * @param t
	 *            a type
	 * @param s
	 *            a type
	 */
	public boolean containsType(Type t, Type s) {
		return containsType.visit(t, s);
	}

	// where
	private TypeRelation containsType = new TypeRelation() {

		private Type U(Type t) {
			while (t.tag == WILDCARD) {
				WildcardType w = (WildcardType) t;
				if (w.isSuperBound())
					return w.bound == null ? syms.objectType : w.bound.bound;
				else
					t = w.type;
			}
			return t;
		}

		private Type L(Type t) {
			while (t.tag == WILDCARD) {
				WildcardType w = (WildcardType) t;
				if (w.isExtendsBound())
					return syms.botType;
				else
					t = w.type;
			}
			return t;
		}

		public Boolean visitType(Type t, Type s) {
			if (s.tag >= firstPartialTag)
				return containedBy(s, t);
			else
				return isSameType(t, s);
		}

		@SuppressWarnings("unused")
		void debugContainsType(WildcardType t, Type s) {
			System.err.println();
			System.err.format(" does %s contain %s?%n", t, s);
			System.err
					.format(" %s U(%s) <: U(%s) %s = %s%n",
							upperBound(s),
							s,
							t,
							U(t),
							t.isSuperBound()
									|| isSubtypeNoCapture(upperBound(s), U(t)));
			System.err.format(
					" %s L(%s) <: L(%s) %s = %s%n",
					L(t),
					t,
					s,
					lowerBound(s),
					t.isExtendsBound()
							|| isSubtypeNoCapture(L(t), lowerBound(s)));
			System.err.println();
		}

		@Override
		public Boolean visitWildcardType(WildcardType t, Type s) {
			if (s.tag >= firstPartialTag)
				return containedBy(s, t);
			else {
				// debugContainsType(t, s);
				return isSameWildcard(t, s)
						|| isCaptureOf(s, t)
						|| ((t.isExtendsBound() || isSubtypeNoCapture(L(t),
								lowerBound(s))) && (t.isSuperBound() || isSubtypeNoCapture(
								upperBound(s), U(t))));
			}
		}

		@Override
		public Boolean visitUndetVar(UndetVar t, Type s) {
			if (s.tag != WILDCARD)
				return isSameType(t, s);
			else
				return false;
		}

		@Override
		public Boolean visitErrorType(ErrorType t, Type s) {
			return true;
		}
	};

	public boolean isCaptureOf(Type s, WildcardType t) {
		if (s.tag != TYPEVAR || !(s instanceof CapturedType))
			return false;
		return isSameWildcard(t, ((CapturedType) s).wildcard);
	}

	public boolean isSameWildcard(WildcardType t, Type s) {
		if (s.tag != WILDCARD)
			return false;
		WildcardType w = (WildcardType) s;
		return w.kind == t.kind && w.type == t.type;
	}

	public boolean containsTypeEquivalent(List<Type> ts, List<Type> ss) {
		while (ts.nonEmpty() && ss.nonEmpty()
				&& containsTypeEquivalent(ts.head, ss.head)) {
			ts = ts.tail;
			ss = ss.tail;
		}
		return ts.isEmpty() && ss.isEmpty();
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isCastable">
	public boolean isCastable(Type t, Type s) {
		return isCastable(t, s, Warner.noWarnings);
	}

	/**
	 * Is t is castable to s?<br>
	 * s is assumed to be an erased type.<br>
	 * (not defined for Method and ForAll types).
	 */
	public boolean isCastable(Type t, Type s, Warner warn) {
		if (t == s)
			return true;

		if (t.isPrimitive() != s.isPrimitive())
			return allowBoxing && isConvertible(t, s, warn);

		if (warn != warnStack.head) {
			try {
				warnStack = warnStack.prepend(warn);
				return isCastable.visit(t, s);
			} finally {
				warnStack = warnStack.tail;
			}
		} else {
			return isCastable.visit(t, s);
		}
	}

	// where
	private TypeRelation isCastable = new TypeRelation() {

		public Boolean visitType(Type t, Type s) {
			if (s.tag == ERROR)
				return true;

			switch (t.tag) {
			case BYTE:
			case CHAR:
			case SHORT:
			case INT:
			case LONG:
			case FLOAT:
			case DOUBLE:
				return s.tag <= DOUBLE;
			case BOOLEAN:
				return s.tag == BOOLEAN;
			case VOID:
				return false;
			case BOT:
				return isSubtype(t, s);
			default:
				throw new AssertionError();
			}
		}

		@Override
		public Boolean visitWildcardType(WildcardType t, Type s) {
			return isCastable(upperBound(t), s, warnStack.head);
		}

		@Override
		public Boolean visitClassType(ClassType t, Type s) {
			if (s.tag == ERROR || s.tag == BOT)
				return true;

			if (s.tag == TYPEVAR) {
				if (isCastable(s.getUpperBound(), t, Warner.noWarnings)) {
					warnStack.head.warnUnchecked();
					return true;
				} else {
					return false;
				}
			}

			if (t.isCompound()) {
				if (!visit(supertype(t), s))
					return false;
				for (Type intf : interfaces(t)) {
					if (!visit(intf, s))
						return false;
				}
				return true;
			}

			if (s.isCompound()) {
				// call recursively to reuse the above code
				return visitClassType((ClassType) s, t);
			}

			if (s.tag == CLASS || s.tag == ARRAY) {
				boolean upcast;
				if ((upcast = isSubtype(erasure(t), erasure(s)))
						|| isSubtype(erasure(s), erasure(t))) {
					if (!upcast && s.tag == ARRAY) {
						if (!isReifiable(s))
							warnStack.head.warnUnchecked();
						return true;
					} else if (s.isRaw()) {
						return true;
					} else if (t.isRaw()) {
						if (!isUnbounded(s))
							warnStack.head.warnUnchecked();
						return true;
					}
					// Assume |a| <: |b|
					final Type a = upcast ? t : s;
					final Type b = upcast ? s : t;
					final boolean HIGH = true;
					final boolean LOW = false;
					final boolean DONT_REWRITE_TYPEVARS = false;
					Type aHigh = rewriteQuantifiers(a, HIGH,
							DONT_REWRITE_TYPEVARS);
					Type aLow = rewriteQuantifiers(a, LOW,
							DONT_REWRITE_TYPEVARS);
					Type bHigh = rewriteQuantifiers(b, HIGH,
							DONT_REWRITE_TYPEVARS);
					Type bLow = rewriteQuantifiers(b, LOW,
							DONT_REWRITE_TYPEVARS);
					Type lowSub = asSub(bLow, aLow.tsym);
					Type highSub = (lowSub == null) ? null : asSub(bHigh,
							aHigh.tsym);
					if (highSub == null) {
						final boolean REWRITE_TYPEVARS = true;
						aHigh = rewriteQuantifiers(a, HIGH, REWRITE_TYPEVARS);
						aLow = rewriteQuantifiers(a, LOW, REWRITE_TYPEVARS);
						bHigh = rewriteQuantifiers(b, HIGH, REWRITE_TYPEVARS);
						bLow = rewriteQuantifiers(b, LOW, REWRITE_TYPEVARS);
						lowSub = asSub(bLow, aLow.tsym);
						highSub = (lowSub == null) ? null : asSub(bHigh,
								aHigh.tsym);
					}
					if (highSub != null) {
						assert a.tsym == highSub.tsym && a.tsym == lowSub.tsym : a.tsym
								+ " != " + highSub.tsym + " != " + lowSub.tsym;
						if (!disjointTypes(aHigh.getTypeArguments(),
								highSub.getTypeArguments())
								&& !disjointTypes(aHigh.getTypeArguments(),
										lowSub.getTypeArguments())
								&& !disjointTypes(aLow.getTypeArguments(),
										highSub.getTypeArguments())
								&& !disjointTypes(aLow.getTypeArguments(),
										lowSub.getTypeArguments())) {
							if (upcast ? giveWarning(a, highSub)
									|| giveWarning(a, lowSub) : giveWarning(
									highSub, a) || giveWarning(lowSub, a))
								warnStack.head.warnUnchecked();
							return true;
						}
					}
					if (isReifiable(s))
						return isSubtypeUnchecked(a, b);
					else
						return isSubtypeUnchecked(a, b, warnStack.head);
				}

				// Sidecast
				if (s.tag == CLASS) {
					if ((s.tsym.flags() & INTERFACE) != 0) {
						return ((t.tsym.flags() & FINAL) == 0) ? sideCast(t, s,
								warnStack.head) : sideCastFinal(t, s,
								warnStack.head);
					} else if ((t.tsym.flags() & INTERFACE) != 0) {
						return ((s.tsym.flags() & FINAL) == 0) ? sideCast(t, s,
								warnStack.head) : sideCastFinal(t, s,
								warnStack.head);
					} else {
						// unrelated class types
						return false;
					}
				}
			}
			return false;
		}

		@Override
		public Boolean visitArrayType(ArrayType t, Type s) {
			switch (s.tag) {
			case ERROR:
			case BOT:
				return true;
			case TYPEVAR:
				if (isCastable(s, t, Warner.noWarnings)) {
					warnStack.head.warnUnchecked();
					return true;
				} else {
					return false;
				}
			case CLASS:
				return isSubtype(t, s);
			case ARRAY:
				if (elemtype(t).tag <= lastBaseTag) {
					return elemtype(t).tag == elemtype(s).tag;
				} else {
					return visit(elemtype(t), elemtype(s));
				}
			default:
				return false;
			}
		}

		@Override
		public Boolean visitTypeVar(TypeVar t, Type s) {
			switch (s.tag) {
			case ERROR:
			case BOT:
				return true;
			case TYPEVAR:
				if (isSubtype(t, s)) {
					return true;
				} else if (isCastable(t.bound, s, Warner.noWarnings)) {
					warnStack.head.warnUnchecked();
					return true;
				} else {
					return false;
				}
			default:
				return isCastable(t.bound, s, warnStack.head);
			}
		}

		@Override
		public Boolean visitErrorType(ErrorType t, Type s) {
			return true;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="disjointTypes">
	public boolean disjointTypes(List<Type> ts, List<Type> ss) {
		while (ts.tail != null && ss.tail != null) {
			if (disjointType(ts.head, ss.head))
				return true;
			ts = ts.tail;
			ss = ss.tail;
		}
		return false;
	}

	/**
	 * Two types or wildcards are considered disjoint if it can be proven that
	 * no type can be contained in both. It is conservative in that it is
	 * allowed to say that two types are not disjoint, even though they actually
	 * are.
	 * 
	 * The type C<X> is castable to C<Y> exactly if X and Y are not disjoint.
	 */
	public boolean disjointType(Type t, Type s) {
		return disjointType.visit(t, s);
	}

	// where
	private TypeRelation disjointType = new TypeRelation() {

		private Set<TypePair> cache = new HashSet<TypePair>();

		public Boolean visitType(Type t, Type s) {
			if (s.tag == WILDCARD)
				return visit(s, t);
			else
				return notSoftSubtypeRecursive(t, s)
						|| notSoftSubtypeRecursive(s, t);
		}

		private boolean isCastableRecursive(Type t, Type s) {
			TypePair pair = new TypePair(t, s);
			if (cache.add(pair)) {
				try {
					return Types.this.isCastable(t, s);
				} finally {
					cache.remove(pair);
				}
			} else {
				return true;
			}
		}

		private boolean notSoftSubtypeRecursive(Type t, Type s) {
			TypePair pair = new TypePair(t, s);
			if (cache.add(pair)) {
				try {
					return Types.this.notSoftSubtype(t, s);
				} finally {
					cache.remove(pair);
				}
			} else {
				return false;
			}
		}

		@Override
		public Boolean visitWildcardType(WildcardType t, Type s) {
			if (t.isUnbound())
				return false;

			if (s.tag != WILDCARD) {
				if (t.isExtendsBound())
					return notSoftSubtypeRecursive(s, t.type);
				else
					// isSuperBound()
					return notSoftSubtypeRecursive(t.type, s);
			}

			if (s.isUnbound())
				return false;

			if (t.isExtendsBound()) {
				if (s.isExtendsBound())
					return !isCastableRecursive(t.type, upperBound(s));
				else if (s.isSuperBound())
					return notSoftSubtypeRecursive(lowerBound(s), t.type);
			} else if (t.isSuperBound()) {
				if (s.isExtendsBound())
					return notSoftSubtypeRecursive(t.type, upperBound(s));
			}
			return false;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="lowerBoundArgtypes">
	/**
	 * Returns the lower bounds of the formals of a method.
	 */
	public List<Type> lowerBoundArgtypes(Type t) {
		return map(t.getParameterTypes(), lowerBoundMapping);
	}

	private final Mapping lowerBoundMapping = new Mapping("lowerBound") {
		public Type apply(Type t) {
			return lowerBound(t);
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="notSoftSubtype">
	/**
	 * This relation answers the question: is impossible that something of type
	 * `t' can be a subtype of `s'? This is different from the question
	 * "is `t' not a subtype of `s'?" when type variables are involved: Integer
	 * is not a subtype of T where <T extends Number> but it is not true that
	 * Integer cannot possibly be a subtype of T.
	 */
	public boolean notSoftSubtype(Type t, Type s) {
		if (t == s)
			return false;
		if (t.tag == TYPEVAR) {
			TypeVar tv = (TypeVar) t;
			if (s.tag == TYPEVAR)
				s = s.getUpperBound();
			return !isCastable(tv.bound, s, Warner.noWarnings);
		}
		if (s.tag != WILDCARD)
			s = upperBound(s);
		if (s.tag == TYPEVAR)
			s = s.getUpperBound();
		return !isSubtype(t, s);
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isReifiable">
	public boolean isReifiable(Type t) {
		return isReifiable.visit(t);
	}

	// where
	private UnaryVisitor<Boolean> isReifiable = new UnaryVisitor<Boolean>() {

		public Boolean visitType(Type t, Void ignored) {
			return true;
		}

		@Override
		public Boolean visitClassType(ClassType t, Void ignored) {
			if (!t.isParameterized())
				return true;

			for (Type param : t.allparams()) {
				if (!param.isUnbound())
					return false;
			}
			return true;
		}

		@Override
		public Boolean visitArrayType(ArrayType t, Void ignored) {
			return visit(t.elemtype);
		}

		@Override
		public Boolean visitTypeVar(TypeVar t, Void ignored) {
			return false;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="Array Utils">
	public boolean isArray(Type t) {
		while (t.tag == WILDCARD)
			t = upperBound(t);
		return t.tag == ARRAY;
	}

	/**
	 * The element type of an array.
	 */
	public Type elemtype(Type t) {
		switch (t.tag) {
		case WILDCARD:
			return elemtype(upperBound(t));
		case ARRAY:
			return ((ArrayType) t).elemtype;
		case FORALL:
			return elemtype(((ForAll) t).qtype);
		case ERROR:
			return t;
		default:
			return null;
		}
	}

	/**
	 * Mapping to take element type of an arraytype
	 */
	private Mapping elemTypeFun = new Mapping("elemTypeFun") {
		public Type apply(Type t) {
			return elemtype(t);
		}
	};

	/**
	 * The number of dimensions of an array type.
	 */
	public int dimensions(Type t) {
		int result = 0;
		while (t.tag == ARRAY) {
			result++;
			t = elemtype(t);
		}
		return result;
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="asSuper">
	/**
	 * Return the (most specific) base type of t that starts with the given
	 * symbol. If none exists, return null.
	 * 
	 * @param t
	 *            a type
	 * @param sym
	 *            a symbol
	 */
	public Type asSuper(Type t, Symbol sym) {
		return asSuper.visit(t, sym);
	}

	// where
	private SimpleVisitor<Type, Symbol> asSuper = new SimpleVisitor<Type, Symbol>() {

		public Type visitType(Type t, Symbol sym) {
			return null;
		}

		@Override
		public Type visitClassType(ClassType t, Symbol sym) {
			if (t.tsym == sym)
				return t;

			Type st = supertype(t);
			if (st.tag == CLASS || st.tag == ERROR) {
				Type x = asSuper(st, sym);
				if (x != null)
					return x;
			}
			if ((sym.flags() & INTERFACE) != 0) {
				for (List<Type> l = interfaces(t); l.nonEmpty(); l = l.tail) {
					Type x = asSuper(l.head, sym);
					if (x != null)
						return x;
				}
			}
			return null;
		}

		@Override
		public Type visitArrayType(ArrayType t, Symbol sym) {
			return isSubtype(t, sym.type) ? sym.type : null;
		}

		@Override
		public Type visitTypeVar(TypeVar t, Symbol sym) {
			return asSuper(t.bound, sym);
		}

		@Override
		public Type visitErrorType(ErrorType t, Symbol sym) {
			return t;
		}
	};

	/**
	 * Return the base type of t or any of its outer types that starts with the
	 * given symbol. If none exists, return null.
	 * 
	 * @param t
	 *            a type
	 * @param sym
	 *            a symbol
	 */
	public Type asOuterSuper(Type t, Symbol sym) {
		switch (t.tag) {
		case CLASS:
			do {
				Type s = asSuper(t, sym);
				if (s != null)
					return s;
				t = t.getEnclosingType();
			} while (t.tag == CLASS);
			return null;
		case ARRAY:
			return isSubtype(t, sym.type) ? sym.type : null;
		case TYPEVAR:
			return asSuper(t, sym);
		case ERROR:
			return t;
		default:
			return null;
		}
	}

	/**
	 * Return the base type of t or any of its enclosing types that starts with
	 * the given symbol. If none exists, return null.
	 * 
	 * @param t
	 *            a type
	 * @param sym
	 *            a symbol
	 */
	public Type asEnclosingSuper(Type t, Symbol sym) {
		switch (t.tag) {
		case CLASS:
			do {
				Type s = asSuper(t, sym);
				if (s != null)
					return s;
				Type outer = t.getEnclosingType();
				t = (outer.tag == CLASS) ? outer
						: (t.tsym.owner.enclClass() != null) ? t.tsym.owner
								.enclClass().type : Type.noType;
			} while (t.tag == CLASS);
			return null;
		case ARRAY:
			return isSubtype(t, sym.type) ? sym.type : null;
		case TYPEVAR:
			return asSuper(t, sym);
		case ERROR:
			return t;
		default:
			return null;
		}
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="memberType">
	/**
	 * The type of given symbol, seen as a member of t.
	 * 
	 * @param t
	 *            a type
	 * @param sym
	 *            a symbol
	 */
	public Type memberType(Type t, Symbol sym) {
		return (sym.flags() & STATIC) != 0 ? sym.type : memberType
				.visit(t, sym);
	}

	// where
	private SimpleVisitor<Type, Symbol> memberType = new SimpleVisitor<Type, Symbol>() {

		public Type visitType(Type t, Symbol sym) {
			return sym.type;
		}

		@Override
		public Type visitWildcardType(WildcardType t, Symbol sym) {
			return memberType(upperBound(t), sym);
		}

		@Override
		public Type visitClassType(ClassType t, Symbol sym) {
			Symbol owner = sym.owner;
			long flags = sym.flags();
			if (((flags & STATIC) == 0) && owner.type.isParameterized()) {
				Type base = asOuterSuper(t, owner);
				if (base != null) {
					List<Type> ownerParams = owner.type.allparams();
					List<Type> baseParams = base.allparams();
					if (ownerParams.nonEmpty()) {
						if (baseParams.isEmpty()) {
							// then base is a raw type
							return erasure(sym.type);
						} else {
							return subst(sym.type, ownerParams, baseParams);
						}
					}
				}
			}
			return sym.type;
		}

		@Override
		public Type visitTypeVar(TypeVar t, Symbol sym) {
			return memberType(t.bound, sym);
		}

		@Override
		public Type visitErrorType(ErrorType t, Symbol sym) {
			return t;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isAssignable">
	public boolean isAssignable(Type t, Type s) {
		return isAssignable(t, s, Warner.noWarnings);
	}

	/**
	 * Is t assignable to s?<br>
	 * Equivalent to subtype except for constant values and raw types.<br>
	 * (not defined for Method and ForAll types)
	 */
	public boolean isAssignable(Type t, Type s, Warner warn) {
		if (t.tag == ERROR)
			return true;
		if (t.tag <= INT && t.constValue() != null) {
			int value = ((Number) t.constValue()).intValue();
			switch (s.tag) {
			case BYTE:
				if (Byte.MIN_VALUE <= value && value <= Byte.MAX_VALUE)
					return true;
				break;
			case CHAR:
				if (Character.MIN_VALUE <= value
						&& value <= Character.MAX_VALUE)
					return true;
				break;
			case SHORT:
				if (Short.MIN_VALUE <= value && value <= Short.MAX_VALUE)
					return true;
				break;
			case INT:
				return true;
			case CLASS:
				switch (unboxedType(s).tag) {
				case BYTE:
				case CHAR:
				case SHORT:
					return isAssignable(t, unboxedType(s), warn);
				}
				break;
			}
		}
		return isConvertible(t, s, warn);
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="erasure">
	/**
	 * The erasure of t {@code |t|} -- the type that results when all type
	 * parameters in t are deleted.
	 */
	public Type erasure(Type t) {
		if (t.tag <= lastBaseTag)
			return t; /* fast special case */
		else
			return erasure.visit(t);
	}

	// where
	private UnaryVisitor<Type> erasure = new UnaryVisitor<Type>() {
		public Type visitType(Type t, Void ignored) {
			if (t.tag <= lastBaseTag)
				return t; /* fast special case */
			else
				return t.map(erasureFun);
		}

		@Override
		public Type visitWildcardType(WildcardType t, Void ignored) {
			return erasure(upperBound(t));
		}

		@Override
		public Type visitClassType(ClassType t, Void ignored) {
			return t.tsym.erasure(Types.this);
		}

		@Override
		public Type visitTypeVar(TypeVar t, Void ignored) {
			return erasure(t.bound);
		}

		@Override
		public Type visitErrorType(ErrorType t, Void ignored) {
			return t;
		}
	};
	private Mapping erasureFun = new Mapping("erasure") {
		public Type apply(Type t) {
			return erasure(t);
		}
	};

	public List<Type> erasure(List<Type> ts) {
		return Type.map(ts, erasureFun);
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="makeCompoundType">
	/**
	 * Make a compound type from non-empty list of types
	 * 
	 * @param bounds
	 *            the types from which the compound type is formed
	 * @param supertype
	 *            is objectType if all bounds are interfaces, null otherwise.
	 */
	public Type makeCompoundType(List<Type> bounds, Type supertype) {
		ClassSymbol bc = new ClassSymbol(ABSTRACT | PUBLIC | SYNTHETIC
				| COMPOUND | ACYCLIC, Type.moreInfo ? names.fromString(bounds
				.toString()) : names.empty, syms.noSymbol);
		if (bounds.head.tag == TYPEVAR)
			// error condition, recover
			bc.erasure_field = syms.objectType;
		else
			bc.erasure_field = erasure(bounds.head);
		bc.members_field = new Scope(bc);
		ClassType bt = (ClassType) bc.type;
		bt.allparams_field = List.nil();
		if (supertype != null) {
			bt.supertype_field = supertype;
			bt.interfaces_field = bounds;
		} else {
			bt.supertype_field = bounds.head;
			bt.interfaces_field = bounds.tail;
		}
		assert bt.supertype_field.tsym.completer != null
				|| !bt.supertype_field.isInterface() : bt.supertype_field;
		return bt;
	}

	/**
	 * Same as {@link #makeCompoundType(List,Type)}, except that the second
	 * parameter is computed directly. Note that this might cause a symbol
	 * completion. Hence, this version of makeCompoundType may not be called
	 * during a classfile read.
	 */
	public Type makeCompoundType(List<Type> bounds) {
		Type supertype = (bounds.head.tsym.flags() & INTERFACE) != 0 ? supertype(bounds.head)
				: null;
		return makeCompoundType(bounds, supertype);
	}

	/**
	 * A convenience wrapper for {@link #makeCompoundType(List)}; the arguments
	 * are converted to a list and passed to the other method. Note that this
	 * might cause a symbol completion. Hence, this version of makeCompoundType
	 * may not be called during a classfile read.
	 */
	public Type makeCompoundType(Type bound1, Type bound2) {
		return makeCompoundType(List.of(bound1, bound2));
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="supertype">
	public Type supertype(Type t) {
		return supertype.visit(t);
	}

	// where
	private UnaryVisitor<Type> supertype = new UnaryVisitor<Type>() {

		public Type visitType(Type t, Void ignored) {
			// A note on wildcards: there is no good way to
			// determine a supertype for a super bounded wildcard.
			return null;
		}

		@Override
		public Type visitClassType(ClassType t, Void ignored) {
			if (t.supertype_field == null) {
				Type supertype = ((ClassSymbol) t.tsym).getSuperclass();
				// An interface has no superclass; its supertype is Object.
				if (t.isInterface())
					supertype = ((ClassType) t.tsym.type).supertype_field;
				if (t.supertype_field == null) {
					List<Type> actuals = classBound(t).allparams();
					List<Type> formals = t.tsym.type.allparams();
					if (actuals.isEmpty()) {
						if (formals.isEmpty())
							// Should not happen. See comments below in
							// interfaces
							t.supertype_field = supertype;
						else
							t.supertype_field = erasure(supertype);
					} else {
						t.supertype_field = subst(supertype, formals, actuals);
					}
				}
			}
			return t.supertype_field;
		}

		/**
		 * The supertype is always a class type. If the type variable's bounds
		 * start with a class type, this is also the supertype. Otherwise, the
		 * supertype is java.lang.Object.
		 */
		@Override
		public Type visitTypeVar(TypeVar t, Void ignored) {
			if (t.bound.tag == TYPEVAR
					|| (!t.bound.isCompound() && !t.bound.isInterface())) {
				return t.bound;
			} else {
				return supertype(t.bound);
			}
		}

		@Override
		public Type visitArrayType(ArrayType t, Void ignored) {
			if (t.elemtype.isPrimitive()
					|| isSameType(t.elemtype, syms.objectType))
				return arraySuperType();
			else
				return new ArrayType(supertype(t.elemtype), t.tsym);
		}

		@Override
		public Type visitErrorType(ErrorType t, Void ignored) {
			return t;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="interfaces">
	/**
	 * Return the interfaces implemented by this class.
	 */
	public List<Type> interfaces(Type t) {
		return interfaces.visit(t);
	}

	// where
	private UnaryVisitor<List<Type>> interfaces = new UnaryVisitor<List<Type>>() {

		public List<Type> visitType(Type t, Void ignored) {
			return List.nil();
		}

		@Override
		public List<Type> visitClassType(ClassType t, Void ignored) {
			if (t.interfaces_field == null) {
				List<Type> interfaces = ((ClassSymbol) t.tsym).getInterfaces();
				if (t.interfaces_field == null) {
					// If t.interfaces_field is null, then t must
					// be a parameterized type (not to be confused
					// with a generic type declaration).
					// Terminology:
					// Parameterized type: List<String>
					// Generic type declaration: class List<E> { ... }
					// So t corresponds to List<String> and
					// t.tsym.type corresponds to List<E>.
					// The reason t must be parameterized type is
					// that completion will happen as a side
					// effect of calling
					// ClassSymbol.getInterfaces. Since
					// t.interfaces_field is null after
					// completion, we can assume that t is not the
					// type of a class/interface declaration.
					assert t != t.tsym.type : t.toString();
					List<Type> actuals = t.allparams();
					List<Type> formals = t.tsym.type.allparams();
					if (actuals.isEmpty()) {
						if (formals.isEmpty()) {
							// In this case t is not generic (nor raw).
							// So this should not happen.
							t.interfaces_field = interfaces;
						} else {
							t.interfaces_field = erasure(interfaces);
						}
					} else {
						t.interfaces_field = upperBounds(subst(interfaces,
								formals, actuals));
					}
				}
			}
			return t.interfaces_field;
		}

		@Override
		public List<Type> visitTypeVar(TypeVar t, Void ignored) {
			if (t.bound.isCompound())
				return interfaces(t.bound);

			if (t.bound.isInterface())
				return List.of(t.bound);

			return List.nil();
		}
	};
	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="isDerivedRaw">
	Map<Type, Boolean> isDerivedRawCache = new HashMap<Type, Boolean>();

	public boolean isDerivedRaw(Type t) {
		Boolean result = isDerivedRawCache.get(t);
		if (result == null) {
			result = isDerivedRawInternal(t);
			isDerivedRawCache.put(t, result);
		}
		return result;
	}

	public boolean isDerivedRawInternal(Type t) {
		if (t.isErroneous())
			return false;
		return t.isRaw() || supertype(t) != null && isDerivedRaw(supertype(t))
				|| isDerivedRaw(interfaces(t));
	}

	public boolean isDerivedRaw(List<Type> ts) {
		List<Type> l = ts;
		while (l.nonEmpty() && !isDerivedRaw(l.head))
			l = l.tail;
		return l.nonEmpty();
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="setBounds">
	/**
	 * Set the bounds field of the given type variable to reflect a (possibly
	 * multiple) list of bounds.
	 * 
	 * @param t
	 *            a type variable
	 * @param bounds
	 *            the bounds, must be nonempty
	 * @param supertype
	 *            is objectType if all bounds are interfaces, null otherwise.
	 */
	public void setBounds(TypeVar t, List<Type> bounds, Type supertype) {
		if (bounds.tail.isEmpty())
			t.bound = bounds.head;
		else
			t.bound = makeCompoundType(bounds, supertype);
		t.rank_field = -1;
	}

	/**
	 * Same as {@link #setBounds(Type.TypeVar,List,Type)}, except that third
	 * parameter is computed directly. Note that this test might cause a symbol
	 * completion. Hence, this version of setBounds may not be called during a
	 * classfile read.
	 */
	public void setBounds(TypeVar t, List<Type> bounds) {
		Type supertype = (bounds.head.tsym.flags() & INTERFACE) != 0 ? supertype(bounds.head)
				: null;
		setBounds(t, bounds, supertype);
		t.rank_field = -1;
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="getBounds">
	/**
	 * Return list of bounds of the given type variable.
	 */
	public List<Type> getBounds(TypeVar t) {
		if (t.bound.isErroneous() || !t.bound.isCompound())
			return List.of(t.bound);
		else if ((erasure(t).tsym.flags() & INTERFACE) == 0)
			return interfaces(t).prepend(supertype(t));
		else
			// No superclass was given in bounds.
			// In this case, supertype is Object, erasure is first interface.
			return interfaces(t);
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="classBound">
	/**
	 * If the given type is a (possibly selected) type variable, return the
	 * bounding class of this type, otherwise return the type itself.
	 */
	public Type classBound(Type t) {
		return classBound.visit(t);
	}

	// where
	private UnaryVisitor<Type> classBound = new UnaryVisitor<Type>() {

		public Type visitType(Type t, Void ignored) {
			return t;
		}

		@Override
		public Type visitClassType(ClassType t, Void ignored) {
			Type outer1 = classBound(t.getEnclosingType());
			if (outer1 != t.getEnclosingType())
				return new ClassType(outer1, t.getTypeArguments(), t.tsym);
			else
				return t;
		}

		@Override
		public Type visitTypeVar(TypeVar t, Void ignored) {
			return classBound(supertype(t));
		}

		@Override
		public Type visitErrorType(ErrorType t, Void ignored) {
			return t;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed"
	// desc="sub signature / override equivalence">
	/**
	 * Returns true iff the first signature is a <em>sub
	 * signature</em> of the other. This is <b>not</b> an equivalence relation.
	 * 
	 * @see "The Java Language Specification, Third Ed. (8.4.2)."
	 * @see #overrideEquivalent(Type t, Type s)
	 * @param t
	 *            first signature (possibly raw).
	 * @param s
	 *            second signature (could be subjected to erasure).
	 * @return true if t is a sub signature of s.
	 */
	public boolean isSubSignature(Type t, Type s) {
		return hasSameArgs(t, s) || hasSameArgs(t, erasure(s));
	}

	/**
	 * Returns true iff these signatures are related by <em>override
	 * equivalence</em>. This is the natural extension of isSubSignature to an
	 * equivalence relation.
	 * 
	 * @see "The Java Language Specification, Third Ed. (8.4.2)."
	 * @see #isSubSignature(Type t, Type s)
	 * @param t
	 *            a signature (possible raw, could be subjected to erasure).
	 * @param s
	 *            a signature (possible raw, could be subjected to erasure).
	 * @return true if either argument is a sub signature of the other.
	 */
	public boolean overrideEquivalent(Type t, Type s) {
		return hasSameArgs(t, s) || hasSameArgs(t, erasure(s))
				|| hasSameArgs(erasure(t), s);
	}

	/**
	 * Does t have the same arguments as s? It is assumed that both types are
	 * (possibly polymorphic) method types. Monomorphic method types
	 * "have the same arguments", if their argument lists are equal. Polymorphic
	 * method types "have the same arguments", if they have the same arguments
	 * after renaming all type variables of one to corresponding type variables
	 * in the other, where correspondence is by position in the type parameter
	 * list.
	 */
	public boolean hasSameArgs(Type t, Type s) {
		return hasSameArgs.visit(t, s);
	}

	// where
	private TypeRelation hasSameArgs = new TypeRelation() {

		public Boolean visitType(Type t, Type s) {
			throw new AssertionError();
		}

		@Override
		public Boolean visitMethodType(MethodType t, Type s) {
			return s.tag == METHOD
					&& containsTypeEquivalent(t.argtypes, s.getParameterTypes());
		}

		@Override
		public Boolean visitForAll(ForAll t, Type s) {
			if (s.tag != FORALL)
				return false;

			ForAll forAll = (ForAll) s;
			return hasSameBounds(t, forAll)
					&& visit(t.qtype,
							subst(forAll.qtype, forAll.tvars, t.tvars));
		}

		@Override
		public Boolean visitErrorType(ErrorType t, Type s) {
			return false;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="subst">
	public List<Type> subst(List<Type> ts, List<Type> from, List<Type> to) {
		return new Subst(from, to).subst(ts);
	}

	/**
	 * Substitute all occurrences of a type in `from' with the corresponding
	 * type in `to' in 't'. Match lists `from' and `to' from the right: If lists
	 * have different length, discard leading elements of the longer list.
	 */
	public Type subst(Type t, List<Type> from, List<Type> to) {
		return new Subst(from, to).subst(t);
	}

	private class Subst extends UnaryVisitor<Type> {
		List<Type> from;
		List<Type> to;

		public Subst(List<Type> from, List<Type> to) {
			int fromLength = from.length();
			int toLength = to.length();
			while (fromLength > toLength) {
				fromLength--;
				from = from.tail;
			}
			while (fromLength < toLength) {
				toLength--;
				to = to.tail;
			}
			this.from = from;
			this.to = to;
		}

		Type subst(Type t) {
			if (from.tail == null)
				return t;
			else
				return visit(t);
		}

		List<Type> subst(List<Type> ts) {
			if (from.tail == null)
				return ts;
			@SuppressWarnings("unused")
			boolean wild = false;
			if (ts.nonEmpty() && from.nonEmpty()) {
				Type head1 = subst(ts.head);
				List<Type> tail1 = subst(ts.tail);
				if (head1 != ts.head || tail1 != ts.tail)
					return tail1.prepend(head1);
			}
			return ts;
		}

		public Type visitType(Type t, Void ignored) {
			return t;
		}

		@Override
		public Type visitMethodType(MethodType t, Void ignored) {
			List<Type> argtypes = subst(t.argtypes);
			Type restype = subst(t.restype);
			List<Type> thrown = subst(t.thrown);
			if (argtypes == t.argtypes && restype == t.restype
					&& thrown == t.thrown)
				return t;
			else
				return new MethodType(argtypes, restype, thrown, t.tsym);
		}

		@Override
		public Type visitTypeVar(TypeVar t, Void ignored) {
			for (List<Type> from = this.from, to = this.to; from.nonEmpty(); from = from.tail, to = to.tail) {
				if (t == from.head) {
					return to.head.withTypeVar(t);
				}
			}
			return t;
		}

		@Override
		public Type visitClassType(ClassType t, Void ignored) {
			if (!t.isCompound()) {
				List<Type> typarams = t.getTypeArguments();
				List<Type> typarams1 = subst(typarams);
				Type outer = t.getEnclosingType();
				Type outer1 = subst(outer);
				if (typarams1 == typarams && outer1 == outer)
					return t;
				else
					return new ClassType(outer1, typarams1, t.tsym);
			} else {
				Type st = subst(supertype(t));
				List<Type> is = upperBounds(subst(interfaces(t)));
				if (st == supertype(t) && is == interfaces(t))
					return t;
				else
					return makeCompoundType(is.prepend(st));
			}
		}

		@Override
		public Type visitWildcardType(WildcardType t, Void ignored) {
			Type bound = t.type;
			if (t.kind != BoundKind.UNBOUND)
				bound = subst(bound);
			if (bound == t.type) {
				return t;
			} else {
				if (t.isExtendsBound() && bound.isExtendsBound())
					bound = upperBound(bound);
				return new WildcardType(bound, t.kind, syms.boundClass, t.bound);
			}
		}

		@Override
		public Type visitArrayType(ArrayType t, Void ignored) {
			Type elemtype = subst(t.elemtype);
			if (elemtype == t.elemtype)
				return t;
			else
				return new ArrayType(upperBound(elemtype), t.tsym);
		}

		@Override
		public Type visitForAll(ForAll t, Void ignored) {
			List<Type> tvars1 = substBounds(t.tvars, from, to);
			Type qtype1 = subst(t.qtype);
			if (tvars1 == t.tvars && qtype1 == t.qtype) {
				return t;
			} else if (tvars1 == t.tvars) {
				return new ForAll(tvars1, qtype1);
			} else {
				return new ForAll(tvars1, Types.this.subst(qtype1, t.tvars,
						tvars1));
			}
		}

		@Override
		public Type visitErrorType(ErrorType t, Void ignored) {
			return t;
		}
	}

	public List<Type> substBounds(List<Type> tvars, List<Type> from,
			List<Type> to) {
		if (tvars.isEmpty())
			return tvars;
		if (tvars.tail.isEmpty())
			// fast common case
			return List.<Type> of(substBound((TypeVar) tvars.head, from, to));
		ListBuffer<Type> newBoundsBuf = lb();
		boolean changed = false;
		// calculate new bounds
		for (Type t : tvars) {
			TypeVar tv = (TypeVar) t;
			Type bound = subst(tv.bound, from, to);
			if (bound != tv.bound)
				changed = true;
			newBoundsBuf.append(bound);
		}
		if (!changed)
			return tvars;
		ListBuffer<Type> newTvars = lb();
		// create new type variables without bounds
		for (Type t : tvars) {
			newTvars.append(new TypeVar(t.tsym, null, syms.botType));
		}
		// the new bounds should use the new type variables in place
		// of the old
		List<Type> newBounds = newBoundsBuf.toList();
		from = tvars;
		to = newTvars.toList();
		for (; !newBounds.isEmpty(); newBounds = newBounds.tail) {
			newBounds.head = subst(newBounds.head, from, to);
		}
		newBounds = newBoundsBuf.toList();
		// set the bounds of new type variables to the new bounds
		for (Type t : newTvars.toList()) {
			TypeVar tv = (TypeVar) t;
			tv.bound = newBounds.head;
			newBounds = newBounds.tail;
		}
		return newTvars.toList();
	}

	public TypeVar substBound(TypeVar t, List<Type> from, List<Type> to) {
		Type bound1 = subst(t.bound, from, to);
		if (bound1 == t.bound)
			return t;
		else
			return new TypeVar(t.tsym, bound1, syms.botType);
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="hasSameBounds">
	/**
	 * Does t have the same bounds for quantified variables as s?
	 */
	boolean hasSameBounds(ForAll t, ForAll s) {
		List<Type> l1 = t.tvars;
		List<Type> l2 = s.tvars;
		while (l1.nonEmpty()
				&& l2.nonEmpty()
				&& isSameType(l1.head.getUpperBound(),
						subst(l2.head.getUpperBound(), s.tvars, t.tvars))) {
			l1 = l1.tail;
			l2 = l2.tail;
		}
		return l1.isEmpty() && l2.isEmpty();
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="newInstances">
	/**
	 * Create new vector of type variables from list of variables changing all
	 * recursive bounds from old to new list.
	 */
	public List<Type> newInstances(List<Type> tvars) {
		List<Type> tvars1 = Type.map(tvars, newInstanceFun);
		for (List<Type> l = tvars1; l.nonEmpty(); l = l.tail) {
			TypeVar tv = (TypeVar) l.head;
			tv.bound = subst(tv.bound, tvars, tvars1);
		}
		return tvars1;
	}

	static private Mapping newInstanceFun = new Mapping("newInstanceFun") {
		public Type apply(Type t) {
			return new TypeVar(t.tsym, t.getUpperBound(), t.getLowerBound());
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="rank">
	/**
	 * The rank of a class is the length of the longest path between the class
	 * and java.lang.Object in the class inheritance graph. Undefined for all
	 * but reference types.
	 */
	public int rank(Type t) {
		switch (t.tag) {
		case CLASS: {
			ClassType cls = (ClassType) t;
			if (cls.rank_field < 0) {
				Name fullname = cls.tsym.getQualifiedName();
				if (fullname == fullname.table.java_lang_Object)
					cls.rank_field = 0;
				else {
					int r = rank(supertype(cls));
					for (List<Type> l = interfaces(cls); l.nonEmpty(); l = l.tail) {
						if (rank(l.head) > r)
							r = rank(l.head);
					}
					cls.rank_field = r + 1;
				}
			}
			return cls.rank_field;
		}
		case TYPEVAR: {
			TypeVar tvar = (TypeVar) t;
			if (tvar.rank_field < 0) {
				int r = rank(supertype(tvar));
				for (List<Type> l = interfaces(tvar); l.nonEmpty(); l = l.tail) {
					if (rank(l.head) > r)
						r = rank(l.head);
				}
				tvar.rank_field = r + 1;
			}
			return tvar.rank_field;
		}
		case ERROR:
			return 0;
		default:
			throw new AssertionError();
		}
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="toString">
	/**
	 * This toString is slightly more descriptive than the one on Type.
	 */
	public String toString(Type t) {
		if (t.tag == FORALL) {
			ForAll forAll = (ForAll) t;
			return typaramsString(forAll.tvars) + forAll.qtype;
		}
		return "" + t;
	}

	// where
	private String typaramsString(List<Type> tvars) {
		StringBuffer s = new StringBuffer();
		s.append('<');
		boolean first = true;
		for (Type t : tvars) {
			if (!first)
				s.append(", ");
			first = false;
			appendTyparamString(((TypeVar) t), s);
		}
		s.append('>');
		return s.toString();
	}

	private void appendTyparamString(TypeVar t, StringBuffer buf) {
		buf.append(t);
		if (t.bound == null
				|| t.bound.tsym.getQualifiedName() == names.java_lang_Object)
			return;
		buf.append(" extends "); // Java syntax; no need for i18n
		Type bound = t.bound;
		if (!bound.isCompound()) {
			buf.append(bound);
		} else if ((erasure(t).tsym.flags() & INTERFACE) == 0) {
			buf.append(supertype(t));
			for (Type intf : interfaces(t)) {
				buf.append('&');
				buf.append(intf);
			}
		} else {
			// No superclass was given in bounds.
			// In this case, supertype is Object, erasure is first interface.
			boolean first = true;
			for (Type intf : interfaces(t)) {
				if (!first)
					buf.append('&');
				first = false;
				buf.append(intf);
			}
		}
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed"
	// desc="Determining least upper bounds of types">
	/**
	 * A cache for closures.
	 * 
	 * <p>
	 * A closure is a list of all the supertypes and interfaces of a class or
	 * interface type, ordered by ClassSymbol.precedes (that is, subclasses come
	 * first, arbitrary but fixed otherwise).
	 */
	private Map<Type, List<Type>> closureCache = new HashMap<Type, List<Type>>();

	/**
	 * Returns the closure of a class or interface type.
	 */
	public List<Type> closure(Type t) {
		List<Type> cl = closureCache.get(t);
		if (cl == null) {
			Type st = supertype(t);
			if (!t.isCompound()) {
				if (st.tag == CLASS) {
					cl = insert(closure(st), t);
				} else if (st.tag == TYPEVAR) {
					cl = closure(st).prepend(t);
				} else {
					cl = List.of(t);
				}
			} else {
				cl = closure(supertype(t));
			}
			for (List<Type> l = interfaces(t); l.nonEmpty(); l = l.tail)
				cl = union(cl, closure(l.head));
			closureCache.put(t, cl);
		}
		return cl;
	}

	/**
	 * Insert a type in a closure
	 */
	public List<Type> insert(List<Type> cl, Type t) {
		if (cl.isEmpty() || t.tsym.precedes(cl.head.tsym, this)) {
			return cl.prepend(t);
		} else if (cl.head.tsym.precedes(t.tsym, this)) {
			return insert(cl.tail, t).prepend(cl.head);
		} else {
			return cl;
		}
	}

	/**
	 * Form the union of two closures
	 */
	public List<Type> union(List<Type> cl1, List<Type> cl2) {
		if (cl1.isEmpty()) {
			return cl2;
		} else if (cl2.isEmpty()) {
			return cl1;
		} else if (cl1.head.tsym.precedes(cl2.head.tsym, this)) {
			return union(cl1.tail, cl2).prepend(cl1.head);
		} else if (cl2.head.tsym.precedes(cl1.head.tsym, this)) {
			return union(cl1, cl2.tail).prepend(cl2.head);
		} else {
			return union(cl1.tail, cl2.tail).prepend(cl1.head);
		}
	}

	/**
	 * Intersect two closures
	 */
	public List<Type> intersect(List<Type> cl1, List<Type> cl2) {
		if (cl1 == cl2)
			return cl1;
		if (cl1.isEmpty() || cl2.isEmpty())
			return List.nil();
		if (cl1.head.tsym.precedes(cl2.head.tsym, this))
			return intersect(cl1.tail, cl2);
		if (cl2.head.tsym.precedes(cl1.head.tsym, this))
			return intersect(cl1, cl2.tail);
		if (isSameType(cl1.head, cl2.head))
			return intersect(cl1.tail, cl2.tail).prepend(cl1.head);
		if (cl1.head.tsym == cl2.head.tsym && cl1.head.tag == CLASS
				&& cl2.head.tag == CLASS) {
			if (cl1.head.isParameterized() && cl2.head.isParameterized()) {
				Type merge = merge(cl1.head, cl2.head);
				return intersect(cl1.tail, cl2.tail).prepend(merge);
			}
			if (cl1.head.isRaw() || cl2.head.isRaw())
				return intersect(cl1.tail, cl2.tail).prepend(erasure(cl1.head));
		}
		return intersect(cl1.tail, cl2.tail);
	}

	// where
	class TypePair {
		final Type t1;
		final Type t2;

		TypePair(Type t1, Type t2) {
			this.t1 = t1;
			this.t2 = t2;
		}

		@SuppressWarnings("static-access")
		@Override
		public int hashCode() {
			return 127 * Types.this.hashCode(t1) + Types.this.hashCode(t2);
		}

		@Override
		public boolean equals(Object obj) {
			if (!(obj instanceof TypePair))
				return false;
			TypePair typePair = (TypePair) obj;
			return isSameType(t1, typePair.t1) && isSameType(t2, typePair.t2);
		}
	}

	Set<TypePair> mergeCache = new HashSet<TypePair>();

	private Type merge(Type c1, Type c2) {
		ClassType class1 = (ClassType) c1;
		List<Type> act1 = class1.getTypeArguments();
		ClassType class2 = (ClassType) c2;
		List<Type> act2 = class2.getTypeArguments();
		ListBuffer<Type> merged = new ListBuffer<Type>();
		List<Type> typarams = class1.tsym.type.getTypeArguments();

		while (act1.nonEmpty() && act2.nonEmpty() && typarams.nonEmpty()) {
			if (containsType(act1.head, act2.head)) {
				merged.append(act1.head);
			} else if (containsType(act2.head, act1.head)) {
				merged.append(act2.head);
			} else {
				TypePair pair = new TypePair(c1, c2);
				Type m;
				if (mergeCache.add(pair)) {
					m = new WildcardType(lub(upperBound(act1.head),
							upperBound(act2.head)), BoundKind.EXTENDS,
							syms.boundClass);
					mergeCache.remove(pair);
				} else {
					m = new WildcardType(syms.objectType, BoundKind.UNBOUND,
							syms.boundClass);
				}
				merged.append(m.withTypeVar(typarams.head));
			}
			act1 = act1.tail;
			act2 = act2.tail;
			typarams = typarams.tail;
		}
		assert (act1.isEmpty() && act2.isEmpty() && typarams.isEmpty());
		return new ClassType(class1.getEnclosingType(), merged.toList(),
				class1.tsym);
	}

	/**
	 * Return the minimum type of a closure, a compound type if no unique
	 * minimum exists.
	 */
	private Type compoundMin(List<Type> cl) {
		if (cl.isEmpty())
			return syms.objectType;
		List<Type> compound = closureMin(cl);
		if (compound.isEmpty())
			return null;
		else if (compound.tail.isEmpty())
			return compound.head;
		else
			return makeCompoundType(compound);
	}

	/**
	 * Return the minimum types of a closure, suitable for computing compoundMin
	 * or glb.
	 */
	private List<Type> closureMin(List<Type> cl) {
		ListBuffer<Type> classes = lb();
		ListBuffer<Type> interfaces = lb();
		while (!cl.isEmpty()) {
			Type current = cl.head;
			if (current.isInterface())
				interfaces.append(current);
			else
				classes.append(current);
			ListBuffer<Type> candidates = lb();
			for (Type t : cl.tail) {
				if (!isSubtypeNoCapture(current, t))
					candidates.append(t);
			}
			cl = candidates.toList();
		}
		return classes.appendList(interfaces).toList();
	}

	/**
	 * Return the least upper bound of pair of types. if the lub does not exist
	 * return null.
	 */
	public Type lub(Type t1, Type t2) {
		return lub(List.of(t1, t2));
	}

	/**
	 * Return the least upper bound (lub) of set of types. If the lub does not
	 * exist return the type of null (bottom).
	 */
	public Type lub(List<Type> ts) {
		final int ARRAY_BOUND = 1;
		final int CLASS_BOUND = 2;
		int boundkind = 0;
		for (Type t : ts) {
			switch (t.tag) {
			case CLASS:
				boundkind |= CLASS_BOUND;
				break;
			case ARRAY:
				boundkind |= ARRAY_BOUND;
				break;
			case TYPEVAR:
				do {
					t = t.getUpperBound();
				} while (t.tag == TYPEVAR);
				if (t.tag == ARRAY) {
					boundkind |= ARRAY_BOUND;
				} else {
					boundkind |= CLASS_BOUND;
				}
				break;
			default:
				if (t.isPrimitive())
					return syms.botType;
			}
		}
		switch (boundkind) {
		case 0:
			return syms.botType;

		case ARRAY_BOUND:
			// calculate lub(A[], B[])
			List<Type> elements = Type.map(ts, elemTypeFun);
			for (Type t : elements) {
				if (t.isPrimitive()) {
					// if a primitive type is found, then return
					// arraySuperType unless all the types are the
					// same
					Type first = ts.head;
					for (Type s : ts.tail) {
						if (!isSameType(first, s)) {
							// lub(int[], B[]) is Cloneable & Serializable
							return arraySuperType();
						}
					}
					// all the array types are the same, return one
					// lub(int[], int[]) is int[]
					return first;
				}
			}
			// lub(A[], B[]) is lub(A, B)[]
			return new ArrayType(lub(elements), syms.arrayClass);

		case CLASS_BOUND:
			// calculate lub(A, B)
			while (ts.head.tag != CLASS && ts.head.tag != TYPEVAR)
				ts = ts.tail;
			assert !ts.isEmpty();
			List<Type> cl = closure(ts.head);
			for (Type t : ts.tail) {
				if (t.tag == CLASS || t.tag == TYPEVAR)
					cl = intersect(cl, closure(t));
			}
			return compoundMin(cl);

		default:
			// calculate lub(A, B[])
			List<Type> classes = List.of(arraySuperType());
			for (Type t : ts) {
				if (t.tag != ARRAY) // Filter out any arrays
					classes = classes.prepend(t);
			}
			// lub(A, B[]) is lub(A, arraySuperType)
			return lub(classes);
		}
	}

	// where
	private Type arraySuperType = null;

	private Type arraySuperType() {
		// initialized lazily to avoid problems during compiler startup
		if (arraySuperType == null) {
			synchronized (this) {
				if (arraySuperType == null) {
					// JLS 10.8: all arrays implement Cloneable and
					// Serializable.
					arraySuperType = makeCompoundType(
							List.of(syms.serializableType, syms.cloneableType),
							syms.objectType);
				}
			}
		}
		return arraySuperType;
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="Greatest lower bound">
	public Type glb(Type t, Type s) {
		if (s == null)
			return t;
		else if (isSubtypeNoCapture(t, s))
			return t;
		else if (isSubtypeNoCapture(s, t))
			return s;

		List<Type> closure = union(closure(t), closure(s));
		List<Type> bounds = closureMin(closure);

		if (bounds.isEmpty()) { // length == 0
			return syms.objectType;
		} else if (bounds.tail.isEmpty()) { // length == 1
			return bounds.head;
		} else { // length > 1
			int classCount = 0;
			for (Type bound : bounds)
				if (!bound.isInterface())
					classCount++;
			if (classCount > 1)
				return syms.errType;
		}
		return makeCompoundType(bounds);
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="hashCode">
	/**
	 * Compute a hash code on a type.
	 */
	public static int hashCode(Type t) {
		return hashCode.visit(t);
	}

	// where
	private static final UnaryVisitor<Integer> hashCode = new UnaryVisitor<Integer>() {

		public Integer visitType(Type t, Void ignored) {
			return t.tag;
		}

		@Override
		public Integer visitClassType(ClassType t, Void ignored) {
			int result = visit(t.getEnclosingType());
			result *= 127;
			result += t.tsym.flatName().hashCode();
			for (Type s : t.getTypeArguments()) {
				result *= 127;
				result += visit(s);
			}
			return result;
		}

		@Override
		public Integer visitWildcardType(WildcardType t, Void ignored) {
			int result = t.kind.hashCode();
			if (t.type != null) {
				result *= 127;
				result += visit(t.type);
			}
			return result;
		}

		@Override
		public Integer visitArrayType(ArrayType t, Void ignored) {
			return visit(t.elemtype) + 12;
		}

		@Override
		public Integer visitTypeVar(TypeVar t, Void ignored) {
			return System.identityHashCode(t.tsym);
		}

		@Override
		public Integer visitUndetVar(UndetVar t, Void ignored) {
			return System.identityHashCode(t);
		}

		@Override
		public Integer visitErrorType(ErrorType t, Void ignored) {
			return 0;
		}
	};

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="Return-Type-Substitutable">
	/**
	 * Does t have a result that is a subtype of the result type of s, suitable
	 * for covariant returns? It is assumed that both types are (possibly
	 * polymorphic) method types. Monomorphic method types are handled in the
	 * obvious way. Polymorphic method types require renaming all type variables
	 * of one to corresponding type variables in the other, where correspondence
	 * is by position in the type parameter list.
	 */
	public boolean resultSubtype(Type t, Type s, Warner warner) {
		List<Type> tvars = t.getTypeArguments();
		List<Type> svars = s.getTypeArguments();
		Type tres = t.getReturnType();
		Type sres = subst(s.getReturnType(), svars, tvars);
		return covariantReturnType(tres, sres, warner);
	}

	/**
	 * Return-Type-Substitutable.
	 * 
	 * @see <a href="http://java.sun.com/docs/books/jls/">The Java Language
	 *      Specification, Third Ed. (8.4.5)</a>
	 */
	public boolean returnTypeSubstitutable(Type r1, Type r2) {
		if (hasSameArgs(r1, r2))
			return resultSubtype(r1, r2, Warner.noWarnings);
		else
			return covariantReturnType(r1.getReturnType(),
					erasure(r2.getReturnType()), Warner.noWarnings);
	}

	public boolean returnTypeSubstitutable(Type r1, Type r2, Type r2res,
			Warner warner) {
		if (isSameType(r1.getReturnType(), r2res))
			return true;
		if (r1.getReturnType().isPrimitive() || r2res.isPrimitive())
			return false;

		if (hasSameArgs(r1, r2))
			return covariantReturnType(r1.getReturnType(), r2res, warner);
		if (!source.allowCovariantReturns())
			return false;
		if (isSubtypeUnchecked(r1.getReturnType(), r2res, warner))
			return true;
		if (!isSubtype(r1.getReturnType(), erasure(r2res)))
			return false;
		warner.warnUnchecked();
		return true;
	}

	/**
	 * Is t an appropriate return type in an overrider for a method that returns
	 * s?
	 */
	public boolean covariantReturnType(Type t, Type s, Warner warner) {
		return isSameType(t, s) || source.allowCovariantReturns()
				&& !t.isPrimitive() && !s.isPrimitive()
				&& isAssignable(t, s, warner);
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="Box/unbox support">
	/**
	 * Return the class that boxes the given primitive.
	 */
	public ClassSymbol boxedClass(Type t) {
		return reader.enterClass(syms.boxedName[t.tag]);
	}

	/**
	 * Return the primitive type corresponding to a boxed type.
	 */
	public Type unboxedType(Type t) {
		if (allowBoxing) {
			for (int i = 0; i < syms.boxedName.length; i++) {
				Name box = syms.boxedName[i];
				if (box != null && asSuper(t, reader.enterClass(box)) != null)
					return syms.typeOfTag[i];
			}
		}
		return Type.noType;
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="Capture conversion">
	/*
	 * JLS 3rd Ed. 5.1.10 Capture Conversion:
	 * 
	 * Let G name a generic type declaration with n formal type parameters A1
	 * ... An with corresponding bounds U1 ... Un. There exists a capture
	 * conversion from G<T1 ... Tn> to G<S1 ... Sn>, where, for 1 <= i <= n:
	 * 
	 * + If Ti is a wildcard type argument (4.5.1) of the form ? then Si is a
	 * fresh type variable whose upper bound is Ui[A1 := S1, ..., An := Sn] and
	 * whose lower bound is the null type.
	 * 
	 * + If Ti is a wildcard type argument of the form ? extends Bi, then Si is
	 * a fresh type variable whose upper bound is glb(Bi, Ui[A1 := S1, ..., An
	 * := Sn]) and whose lower bound is the null type, where glb(V1,... ,Vm) is
	 * V1 & ... & Vm. It is a compile-time error if for any two classes (not
	 * interfaces) Vi and Vj,Vi is not a subclass of Vj or vice versa.
	 * 
	 * + If Ti is a wildcard type argument of the form ? super Bi, then Si is a
	 * fresh type variable whose upper bound is Ui[A1 := S1, ..., An := Sn] and
	 * whose lower bound is Bi.
	 * 
	 * + Otherwise, Si = Ti.
	 * 
	 * Capture conversion on any type other than a parameterized type (4.5) acts
	 * as an identity conversion (5.1.1). Capture conversions never require a
	 * special action at run time and therefore never throw an exception at run
	 * time.
	 * 
	 * Capture conversion is not applied recursively.
	 */
	/**
	 * Capture conversion as specified by JLS 3rd Ed.
	 */
	public Type capture(Type t) {
		if (t.tag != CLASS)
			return t;
		ClassType cls = (ClassType) t;
		if (cls.isRaw() || !cls.isParameterized())
			return cls;

		ClassType G = (ClassType) cls.asElement().asType();
		List<Type> A = G.getTypeArguments();
		List<Type> T = cls.getTypeArguments();
		List<Type> S = freshTypeVariables(T);

		List<Type> currentA = A;
		List<Type> currentT = T;
		List<Type> currentS = S;
		boolean captured = false;
		while (!currentA.isEmpty() && !currentT.isEmpty()
				&& !currentS.isEmpty()) {
			if (currentS.head != currentT.head) {
				captured = true;
				WildcardType Ti = (WildcardType) currentT.head;
				Type Ui = currentA.head.getUpperBound();
				CapturedType Si = (CapturedType) currentS.head;
				if (Ui == null)
					Ui = syms.objectType;
				switch (Ti.kind) {
				case UNBOUND:
					Si.bound = subst(Ui, A, S);
					Si.lower = syms.botType;
					break;
				case EXTENDS:
					Si.bound = glb(Ti.getExtendsBound(), subst(Ui, A, S));
					Si.lower = syms.botType;
					break;
				case SUPER:
					Si.bound = subst(Ui, A, S);
					Si.lower = Ti.getSuperBound();
					break;
				}
				if (Si.bound == Si.lower)
					currentS.head = Si.bound;
			}
			currentA = currentA.tail;
			currentT = currentT.tail;
			currentS = currentS.tail;
		}
		if (!currentA.isEmpty() || !currentT.isEmpty() || !currentS.isEmpty())
			return erasure(t); // some "rare" type involved

		if (captured)
			return new ClassType(cls.getEnclosingType(), S, cls.tsym);
		else
			return t;
	}

	// where
	private List<Type> freshTypeVariables(List<Type> types) {
		ListBuffer<Type> result = lb();
		for (Type t : types) {
			if (t.tag == WILDCARD) {
				Type bound = ((WildcardType) t).getExtendsBound();
				if (bound == null)
					bound = syms.objectType;
				result.append(new CapturedType(capturedName, syms.noSymbol,
						bound, syms.botType, (WildcardType) t));
			} else {
				result.append(t);
			}
		}
		return result.toList();
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="Internal utility methods">
	private List<Type> upperBounds(List<Type> ss) {
		if (ss.isEmpty())
			return ss;
		Type head = upperBound(ss.head);
		List<Type> tail = upperBounds(ss.tail);
		if (head != ss.head || tail != ss.tail)
			return tail.prepend(head);
		else
			return ss;
	}

	private boolean sideCast(Type from, Type to, Warner warn) {
		// We are casting from type $from$ to type $to$, which are
		// non-final unrelated types. This method
		// tries to reject a cast by transferring type parameters
		// from $to$ to $from$ by common superinterfaces.
		boolean reverse = false;
		Type target = to;
		if ((to.tsym.flags() & INTERFACE) == 0) {
			assert (from.tsym.flags() & INTERFACE) != 0;
			reverse = true;
			to = from;
			from = target;
		}
		List<Type> commonSupers = superClosure(to, erasure(from));
		boolean giveWarning = commonSupers.isEmpty();
		// The arguments to the supers could be unified here to
		// get a more accurate analysis
		while (commonSupers.nonEmpty()) {
			Type t1 = asSuper(from, commonSupers.head.tsym);
			Type t2 = commonSupers.head; // same as asSuper(to,
											// commonSupers.head.tsym);
			if (disjointTypes(t1.getTypeArguments(), t2.getTypeArguments()))
				return false;
			giveWarning = giveWarning
					|| (reverse ? giveWarning(t2, t1) : giveWarning(t1, t2));
			commonSupers = commonSupers.tail;
		}
		if (giveWarning && !isReifiable(to))
			warn.warnUnchecked();
		if (!source.allowCovariantReturns())
			// reject if there is a common method signature with
			// incompatible return types.
			chk.checkCompatibleAbstracts(warn.pos(), from, to);
		return true;
	}

	private boolean sideCastFinal(Type from, Type to, Warner warn) {
		// We are casting from type $from$ to type $to$, which are
		// unrelated types one of which is final and the other of
		// which is an interface. This method
		// tries to reject a cast by transferring type parameters
		// from the final class to the interface.
		boolean reverse = false;
		Type target = to;
		if ((to.tsym.flags() & INTERFACE) == 0) {
			assert (from.tsym.flags() & INTERFACE) != 0;
			reverse = true;
			to = from;
			from = target;
		}
		assert (from.tsym.flags() & FINAL) != 0;
		Type t1 = asSuper(from, to.tsym);
		if (t1 == null)
			return false;
		Type t2 = to;
		if (disjointTypes(t1.getTypeArguments(), t2.getTypeArguments()))
			return false;
		if (!source.allowCovariantReturns())
			// reject if there is a common method signature with
			// incompatible return types.
			chk.checkCompatibleAbstracts(warn.pos(), from, to);
		if (!isReifiable(target)
				&& (reverse ? giveWarning(t2, t1) : giveWarning(t1, t2)))
			warn.warnUnchecked();
		return true;
	}

	private boolean giveWarning(Type from, Type to) {
		// To and from are (possibly different) parameterizations
		// of the same class or interface
		return to.isParameterized()
				&& !containsType(to.getTypeArguments(), from.getTypeArguments());
	}

	private List<Type> superClosure(Type t, Type s) {
		List<Type> cl = List.nil();
		for (List<Type> l = interfaces(t); l.nonEmpty(); l = l.tail) {
			if (isSubtype(s, erasure(l.head))) {
				cl = insert(cl, l.head);
			} else {
				cl = union(cl, superClosure(l.head, s));
			}
		}
		return cl;
	}

	private boolean containsTypeEquivalent(Type t, Type s) {
		return isSameType(t, s) || // shortcut
				containsType(t, s) && containsType(s, t);
	}

	/**
	 * Adapt a type by computing a substitution which maps a source type to a
	 * target type.
	 * 
	 * @param source
	 *            the source type
	 * @param target
	 *            the target type
	 * @param from
	 *            the type variables of the computed substitution
	 * @param to
	 *            the types of the computed substitution.
	 */
	public void adapt(Type source, Type target, ListBuffer<Type> from,
			ListBuffer<Type> to) throws AdaptFailure {
		Map<Symbol, Type> mapping = new HashMap<Symbol, Type>();
		adaptRecursive(source, target, from, to, mapping);
		List<Type> fromList = from.toList();
		List<Type> toList = to.toList();
		while (!fromList.isEmpty()) {
			Type val = mapping.get(fromList.head.tsym);
			if (toList.head != val)
				toList.head = val;
			fromList = fromList.tail;
			toList = toList.tail;
		}
	}

	// where
	private void adaptRecursive(Type source, Type target,
			ListBuffer<Type> from, ListBuffer<Type> to,
			Map<Symbol, Type> mapping) throws AdaptFailure {
		if (source.tag == TYPEVAR) {
			// Check to see if there is
			// already a mapping for $source$, in which case
			// the old mapping will be merged with the new
			Type val = mapping.get(source.tsym);
			if (val != null) {
				if (val.isSuperBound() && target.isSuperBound()) {
					val = isSubtype(lowerBound(val), lowerBound(target)) ? target
							: val;
				} else if (val.isExtendsBound() && target.isExtendsBound()) {
					val = isSubtype(upperBound(val), upperBound(target)) ? val
							: target;
				} else if (!isSameType(val, target)) {
					throw new AdaptFailure();
				}
			} else {
				val = target;
				from.append(source);
				to.append(target);
			}
			mapping.put(source.tsym, val);
		} else if (source.tag == target.tag) {
			switch (source.tag) {
			case CLASS:
				adapt(source.allparams(), target.allparams(), from, to, mapping);
				break;
			case ARRAY:
				adaptRecursive(elemtype(source), elemtype(target), from, to,
						mapping);
				break;
			case WILDCARD:
				if (source.isExtendsBound()) {
					adaptRecursive(upperBound(source), upperBound(target),
							from, to, mapping);
				} else if (source.isSuperBound()) {
					adaptRecursive(lowerBound(source), lowerBound(target),
							from, to, mapping);
				}
				break;
			}
		}
	}

	public static class AdaptFailure extends Exception {
		static final long serialVersionUID = -7490231548272701566L;
	}

	/**
	 * Adapt a type by computing a substitution which maps a list of source
	 * types to a list of target types.
	 * 
	 * @param source
	 *            the source type
	 * @param target
	 *            the target type
	 * @param from
	 *            the type variables of the computed substitution
	 * @param to
	 *            the types of the computed substitution.
	 */
	private void adapt(List<Type> source, List<Type> target,
			ListBuffer<Type> from, ListBuffer<Type> to,
			Map<Symbol, Type> mapping) throws AdaptFailure {
		if (source.length() == target.length()) {
			while (source.nonEmpty()) {
				adaptRecursive(source.head, target.head, from, to, mapping);
				source = source.tail;
				target = target.tail;
			}
		}
	}

	private void adaptSelf(Type t, ListBuffer<Type> from, ListBuffer<Type> to) {
		try {
			// if (t.tsym.type != t)
			adapt(t.tsym.type, t, from, to);
		} catch (AdaptFailure ex) {
			// Adapt should never fail calculating a mapping from
			// t.tsym.type to t as there can be no merge problem.
			throw new AssertionError(ex);
		}
	}

	/**
	 * Rewrite all type variables (universal quantifiers) in the given type to
	 * wildcards (existential quantifiers). This is used to determine if a cast
	 * is allowed. For example, if high is true and {@code T <: Number}, then
	 * {@code List<T>} is rewritten to {@code List<?  extends Number>}. Since
	 * {@code List<Integer> <:
	 * List<? extends Number>} a {@code List<T>} can be cast to
	 * {@code List<Integer>} with a warning.
	 * 
	 * @param t
	 *            a type
	 * @param high
	 *            if true return an upper bound; otherwise a lower bound
	 * @param rewriteTypeVars
	 *            only rewrite captured wildcards if false; otherwise rewrite
	 *            all type variables
	 * @return the type rewritten with wildcards (existential quantifiers) only
	 */
	private Type rewriteQuantifiers(Type t, boolean high,
			boolean rewriteTypeVars) {
		return new Rewriter(high, rewriteTypeVars).rewrite(t);
	}

	class Rewriter extends UnaryVisitor<Type> {

		boolean high;
		boolean rewriteTypeVars;

		Rewriter(boolean high, boolean rewriteTypeVars) {
			this.high = high;
			this.rewriteTypeVars = rewriteTypeVars;
		}

		Type rewrite(Type t) {
			ListBuffer<Type> from = new ListBuffer<Type>();
			ListBuffer<Type> to = new ListBuffer<Type>();
			adaptSelf(t, from, to);
			ListBuffer<Type> rewritten = new ListBuffer<Type>();
			List<Type> formals = from.toList();
			boolean changed = false;
			for (Type arg : to.toList()) {
				Type bound = visit(arg);
				if (arg != bound) {
					changed = true;
					bound = high ? makeExtendsWildcard(bound,
							(TypeVar) formals.head) : makeSuperWildcard(bound,
							(TypeVar) formals.head);
				}
				rewritten.append(bound);
				formals = formals.tail;
			}
			if (changed)
				return subst(t.tsym.type, from.toList(), rewritten.toList());
			else
				return t;
		}

		public Type visitType(Type t, Void s) {
			return high ? upperBound(t) : lowerBound(t);
		}

		@Override
		public Type visitCapturedType(CapturedType t, Void s) {
			return visitWildcardType(t.wildcard, null);
		}

		@Override
		public Type visitTypeVar(TypeVar t, Void s) {
			if (rewriteTypeVars)
				return high ? t.bound : syms.botType;
			else
				return t;
		}

		@Override
		public Type visitWildcardType(WildcardType t, Void s) {
			Type bound = high ? t.getExtendsBound() : t.getSuperBound();
			if (bound == null)
				bound = high ? syms.objectType : syms.botType;
			return bound;
		}
	}

	/**
	 * Create a wildcard with the given upper (extends) bound; create an
	 * unbounded wildcard if bound is Object.
	 * 
	 * @param bound
	 *            the upper bound
	 * @param formal
	 *            the formal type parameter that will be substituted by the
	 *            wildcard
	 */
	private WildcardType makeExtendsWildcard(Type bound, TypeVar formal) {
		if (bound == syms.objectType) {
			return new WildcardType(syms.objectType, BoundKind.UNBOUND,
					syms.boundClass, formal);
		} else {
			return new WildcardType(bound, BoundKind.EXTENDS, syms.boundClass,
					formal);
		}
	}

	/**
	 * Create a wildcard with the given lower (super) bound; create an unbounded
	 * wildcard if bound is bottom (type of {@code null}).
	 * 
	 * @param bound
	 *            the lower bound
	 * @param formal
	 *            the formal type parameter that will be substituted by the
	 *            wildcard
	 */
	private WildcardType makeSuperWildcard(Type bound, TypeVar formal) {
		if (bound.tag == BOT) {
			return new WildcardType(syms.objectType, BoundKind.UNBOUND,
					syms.boundClass, formal);
		} else {
			return new WildcardType(bound, BoundKind.SUPER, syms.boundClass,
					formal);
		}
	}

	/**
	 * A wrapper for a type that allows use in sets.
	 */
	class SingletonType {
		final Type t;

		SingletonType(Type t) {
			this.t = t;
		}

		@SuppressWarnings("static-access")
		public int hashCode() {
			return Types.this.hashCode(t);
		}

		public boolean equals(Object obj) {
			return (obj instanceof SingletonType)
					&& isSameType(t, ((SingletonType) obj).t);
		}

		public String toString() {
			return t.toString();
		}
	}

	// </editor-fold>

	// <editor-fold defaultstate="collapsed" desc="Visitors">
	/**
	 * A default visitor for types. All visitor methods except visitType are
	 * implemented by delegating to visitType. Concrete subclasses must provide
	 * an implementation of visitType and can override other methods as needed.
	 * 
	 * @param <R>
	 *            the return type of the operation implemented by this visitor;
	 *            use Void if no return type is needed.
	 * @param <S>
	 *            the type of the second argument (the first being the type
	 *            itself) of the operation implemented by this visitor; use Void
	 *            if a second argument is not needed.
	 */
	public static abstract class DefaultTypeVisitor<R, S> implements
			Type.Visitor<R, S> {
		final public R visit(Type t, S s) {
			return t.accept(this, s);
		}

		public R visitClassType(ClassType t, S s) {
			return visitType(t, s);
		}

		public R visitWildcardType(WildcardType t, S s) {
			return visitType(t, s);
		}

		public R visitArrayType(ArrayType t, S s) {
			return visitType(t, s);
		}

		public R visitMethodType(MethodType t, S s) {
			return visitType(t, s);
		}

		public R visitPackageType(PackageType t, S s) {
			return visitType(t, s);
		}

		public R visitTypeVar(TypeVar t, S s) {
			return visitType(t, s);
		}

		public R visitCapturedType(CapturedType t, S s) {
			return visitType(t, s);
		}

		public R visitForAll(ForAll t, S s) {
			return visitType(t, s);
		}

		public R visitUndetVar(UndetVar t, S s) {
			return visitType(t, s);
		}

		public R visitErrorType(ErrorType t, S s) {
			return visitType(t, s);
		}
	}

	/**
	 * A <em>simple</em> visitor for types. This visitor is simple as captured
	 * wildcards, for-all types (generic methods), and undetermined type
	 * variables (part of inference) are hidden. Captured wildcards are hidden
	 * by treating them as type variables and the rest are hidden by visiting
	 * their qtypes.
	 * 
	 * @param <R>
	 *            the return type of the operation implemented by this visitor;
	 *            use Void if no return type is needed.
	 * @param <S>
	 *            the type of the second argument (the first being the type
	 *            itself) of the operation implemented by this visitor; use Void
	 *            if a second argument is not needed.
	 */
	public static abstract class SimpleVisitor<R, S> extends
			DefaultTypeVisitor<R, S> {
		@Override
		public R visitCapturedType(CapturedType t, S s) {
			return visitTypeVar(t, s);
		}

		@Override
		public R visitForAll(ForAll t, S s) {
			return visit(t.qtype, s);
		}

		@Override
		public R visitUndetVar(UndetVar t, S s) {
			return visit(t.qtype, s);
		}
	}

	/**
	 * A plain relation on types. That is a 2-ary function on the form
	 * Type&nbsp;&times;&nbsp;Type&nbsp;&rarr;&nbsp;Boolean. <!-- In plain text:
	 * Type x Type -> Boolean -->
	 */
	public static abstract class TypeRelation extends
			SimpleVisitor<Boolean, Type> {
	}

	/**
	 * A convenience visitor for implementing operations that only require one
	 * argument (the type itself), that is, unary operations.
	 * 
	 * @param <R>
	 *            the return type of the operation implemented by this visitor;
	 *            use Void if no return type is needed.
	 */
	public static abstract class UnaryVisitor<R> extends SimpleVisitor<R, Void> {
		final public R visit(Type t) {
			return t.accept(this, null);
		}
	}

	/**
	 * A visitor for implementing a mapping from types to types. The default
	 * behavior of this class is to implement the identity mapping (mapping a
	 * type to itself). This can be overridden in subclasses.
	 * 
	 * @param <S>
	 *            the type of the second argument (the first being the type
	 *            itself) of this mapping; use Void if a second argument is not
	 *            needed.
	 */
	public static class MapVisitor<S> extends DefaultTypeVisitor<Type, S> {
		final public Type visit(Type t) {
			return t.accept(this, null);
		}

		public Type visitType(Type t, S s) {
			return t;
		}
	}
	// </editor-fold>
}
